Suppose that at a competition 15 children received 63 pieces of candy. Show that at least one child received at least 5 pieces of candy.
My prof told me that I could use proof by contradiction, but I forgot what she did. She said something like:
Assume, to the contrary, that each child receives at most 4 pieces of candy. Then ceiling(63/15) = 5, a contradiction.
Is this correct? I just want to know if I recalled the proof correctly.
Thank you.
My prof told me that I could use proof by contradiction, but I forgot what she did. She said something like:
Assume, to the contrary, that each child receives at most 4 pieces of candy. Then ceiling(63/15) = 5, a contradiction.
Is this correct? I just want to know if I recalled the proof correctly.
Thank you.
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On the right lines. Here's how I would put it, not even using the ceiling function:
Assume each child received at most 4 pieces of candy. Then the number of pieces of candy received must be at most 15*4 = 60. But there were 63 pieces of candy received - a contradiction. Hence at least one child received at least 5 pieces of candy.
Your proof is correct, but it seems to be that there is a little bit missing between the assumption and your use of the ceiling that would make it clearer.
Assume each child received at most 4 pieces of candy. Then the number of pieces of candy received must be at most 15*4 = 60. But there were 63 pieces of candy received - a contradiction. Hence at least one child received at least 5 pieces of candy.
Your proof is correct, but it seems to be that there is a little bit missing between the assumption and your use of the ceiling that would make it clearer.